Universal Mechanism of Dynamical Memory in Light-Nuclei Formation and Cosmological Bose-Einstein Condensation

Abstract

We identify a common reduced nonequilibrium structure in light-nuclei formation in heavy-ion collisions and cosmological Bose-Einstein condensation. In the heavy-ion system, eliminating a finite-lived intermediate hadronic sector, represented minimally by the Delta component, generates an exponential memory kernel. In the Fukuyama-Morikawa-Tatekawa (FMT) cosmological system, the localized collapse component is generated from the coherent field and feeds back through the expansion rate, producing the causal sequence rho_phi -> rho_l -> H -> rho_phi. Eliminating this additional dynamical sector likewise generates a history-dependent reduced equation. Although the two memory kernels and their microscopic origins are different, they realize the same generic causal structure: elimination of a dynamically relevant coupled sector leaves a memory of its previous evolution. This defines a reduced-dynamical universality class and gives a time-scale criterion separating approximately Markovian from non-Markovian evolution. As a concrete application, we consider hypertriton formation through direct p+n+Lambda and sequential d+Lambda channels. The direct channel acts as a local source, whereas elimination of the intermediate deuteron sector generates a retarded sequential contribution. We predict that the sequential-to-direct ratio depends on the duration and expansion history of the hadronic stage and increases with effective evolution time when sequential correlations are retained more efficiently. Existing coalescence calculations provide a benchmark in which this ratio changes by about 40% while the total hypertriton abundance changes by only about 20%. More generally, several independent relaxation modes in the eliminated sector generate a multi-scale memory kernel.

arXiv comment14 pages, 4 figures, Substantially revised version. The universal reduced-dynamical structure is derived explicitly, including causal memory kernels in both the heavy-ion and cosmological systems. A new application to hypertriton formation and a testable prediction for the sequential-to-direct formation ratio are included